BRONCHOCYATHOIDEA R. Bedford & J. Bedford, 1936: Outer wall with simple pores.
PRETIOSOCYATHOIDEA Rozanov, 1969: Outer wall with independent microporous sheath.
ERBOCYATHOIDEA Vologdin & Zhuravleva, 1956: Outer wall with attached microporous sheath.
TUMULOCYATHOIDEA Krasnopeeva, 1953: Outer wall with simple tumuli.
LENOCYATHOIDEA Zhuravleva, 1956: Outer wall with multiperforate tumuli.
ANNULOCYATHOIDEA Krasnopeeva, 1953: Outer wall with bracts or scales.
ETHMOPHYLLOIDEA Okulitch, 1937: Outer wall with canals.
TERCYATHOIDEA Vologdin, 1939: Outer wall clathrate.
SIGMOCYATHOIDEA Krasnopeeva, 1953: Outer wall with annuli.